The Radius of a Polymer at a Near-Critical Temperature

TL;DR

This paper analyzes how the size of a polymer modeled with a mean-field approach varies near a critical temperature, considering the effects of temperature and chain length.

Contribution

It introduces a mean-field model to study the dependence of polymer size on temperature and chain length near criticality.

Findings

Polymer size diverges as temperature approaches the critical value.

The model predicts specific scaling laws for polymer size near criticality.

Results provide insights into polymer behavior in critical regimes.

Abstract

We consider a mean-field model of a polymer with a spherically-symmetric finitely supported potential. We describe how the typical size of the polymer depends on the two parameters: the temperature, which approaches the critical value, and the length of the polymer chain, which goes to infinity.